Exams › IBPS PO › Quantitative Aptitude

Q82. Solve both equations and form a new equation in variable 'z' (reduce to the lowest possible factor) using the roots of equations 1 and 2 as per the instructions given below. 1. $2 - \frac{1}{x} + \frac{9}{x^2} = 0$ 2. $(y - 2)^2 = 2\frac{1}{4}$ What will be the new equation if the roots are the highest root of equation 1 and the lowest root of equation 2?

1. 8z² - 34z - 9 = 0
2. 4z² - 20z + 9 = 0
3. 8z² - 20z + 9 = 0
4. 4z² - 34z - 9 = 0
5. None of these

Correct answer: None of these

Solution

Let $t=1/x$. Then $2-t+9t^2=0$ gives roots $t=\frac{1\pm 5i\sqrt{7}}{18}$, so the question as written does not yield real roots. Equation 2 gives $y=2\pm \frac{3}{2}$, i.e. $\frac{1}{2}$ and $\frac{7}{2}$. Since the resulting equation from the stated roots does not match any option, the answer is 'None of these'.

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